Many real-life systems can be modelled as complex networks, where the agents
of the system are represented as nodes and the ties between those agents are
represented as edges. Recent advances in data collection technologies give rise
to various populations of networks, which capture different aspects of the data.
In this thesis we make an essential progress in the modelling and analysis of three
different populations of complex networks.
First, in real-life systems involving measurements obtained from a population of
participants, the system may be described by a population of networks where
each participant is himself described by a whole network. We formulate a relevant genomics problem by constructing such a population of complex networks,
and address a series of biological hypothesis which involve the clustering and
classification of this population of networks.
Second, real-life situations are modelled as a multiplex network where each layer
of the multiplex captures different type of relationships across the same set of
nodes. The nature of the multiplex network raises the question of whether the
same connectivity patterns fit all layers. We use a community detection procedure to address this problem, where random walks on the multiplex are used
to detect shared and non-shared community structures across the layers of the
multiplex.
Third, the interactions between the entities of a system that evolve in time are
formalized as a temporal network. When the number of entities in the network is
very large, different levels of detail and how they change in time are interesting.
We use a multi-scale community detection procedure to solve the problems by
applying spectral graph wavelets on the temporal network to detect changes in
the community structure that occur in more than one scale.